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Sphericalization Preserving Uniformity, Doubling and Poincare Inequality on Metric Measure Spaces

Sphericalization conformally deforms an unbounded metric measure space, via a density function, into a bounded one, generalizing the inverse stereographic projection. This concept identifies sharp conditions on the deforming density under which the transformation preserves uniformity of the space, the doubling property of the measure, and the support of a p-Poincare inequality.

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Sharp conditions for preserving uniformity, doubling measure and Poincar´e inequality under

Sphericalization is a conformal deformation of an unbounded metric measure space by a density function that makes the space bounded, generalizing the inverse stereographic projection that maps the pl…